A Dirac type xp-Model and the Riemann Zeros

Abstract

We propose a Dirac type modification of the xp-model to a $x \slashed{p}$ model on a semi-infinite cylinder. This model is inspired by recent work by Sierra et al on the xp-model on the half-line. Our model realizes the Berry-Keating conjecture on the Riemann zeros. We indicate the connection of our model to that of gapped graphene with a supercritical Coulomb charge, which might provide a physical system for the study of the zeros of the Riemann Zeta function.

5 pages, two-column, substantial modification to the text, new equations added

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Cited by in corpus (7)

• Synthetic Unruh effect in cold atoms
• The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime
• The Riemann zeros as spectrum and the Riemann hypothesis
• An $xp$ model on $Ad{S}_2$ spacetime
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Distribution of xp in some molecular rotational states
• Conformal quantum mechanics and holography in noncommutative space-time